Tropical Storm Chantal was headed for the islands of the eastern Caribbean Sea on Monday, prompting storm warnings from Puerto Rico to Barbados.

The storm was well out in the Atlantic Ocean on Monday night, but it was moving swiftly over the open water and was expected to cross into the Caribbean early Tuesday, U.S. forecasters reported.

Projections from the National Hurricane Center in Miami show Chantal is not expected to reach hurricane strength. But forecasters reported the storm would cross the Lesser Antilles, may skirt Puerto Rico and sweep across the Dominican Republic, Haiti and eastern Cuba on Wednesday and Thursday.

At 8 p.m. ET, Chantal was centered about 320 miles (515 kilometers) east-southeast of Barbados, moving to the west-northwest at 26 mph. Its top winds had strengthened to 50 mph, and the storm could strengthen more in the next two days.

Tropical storm-force winds of 39 mph or higher extended more than 90 miles from the eye, mainly to the north, the hurricane center reported.

Tropical storm warnings were in place for Barbados, Dominica, St. Lucia, Martinique, Guadeloupe and Puerto Rico, while tropical storm watches were posted for the U.S. Virgin Islands, St. Vincent, the southern coast of the Dominican Republic and the islands of Vieques and Culebra, off Puerto Rico.

Chantal is expected to dump 2 to 4 inches of rain over the Leeward and Windward Islands, with up to 6 inches possible in some areas. Storm surges could be as high as 3 feet.

Any threat to the United States was highly uncertain, CNN meteorologist Sherri Pugh said. Computer models aren't clear on whether the storm will turn toward the Gulf Coast, the East Coast or out to sea, she said.

Currently, the hurricane center projects that Chantal will fade to a tropical depression somewhere between Cuba and the Bahamas by Friday.